%   ORIGINAL: 'h4/thm/option/OPTION_MAP2_SOME_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !v o2 o1 f. 'h4/const/option/OPTION_MAP2' f o1 o2 = 'h4/const/option/SOME' v <=> (?x1 x2. o1 = 'h4/const/option/SOME' x1 /\ o2 = 'h4/const/option/SOME' x2 /\ v = f x1 x2)
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !v o2 o1 f. 'h4/const/option/OPTION_MAP2' f o1 o2 = 'h4/const/option/SOME' v <=> (?x1 x2. o1 = 'h4/const/option/SOME' x1 /\ o2 = 'h4/const/option/SOME' x2 /\ v = happ (happ f x1) x2)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f100307,V_3f100303]: ![F, G]: (![X]: s(V_3f100303,happ(s(fun(V_3f100307,V_3f100303),F),s(V_3f100307,X))) = s(V_3f100303,happ(s(fun(V_3f100307,V_3f100303),G),s(V_3f100307,X))) => s(fun(V_3f100307,V_3f100303),F) = s(fun(V_3f100307,V_3f100303),G))).
fof('h4/thm/option/OPTION_MAP2_SOME_', conjecture, ![C,A,B]: ![V, O2, O1, F]: (s('h4/type/option/option'(C),'h4/const/option/OPTION_MAP2'(s(fun(A,fun(B,C)),F),s('h4/type/option/option'(A),O1),s('h4/type/option/option'(B),O2))) = s('h4/type/option/option'(C),'h4/const/option/SOME'(s(C,V))) <=> ?[X1, X2]: (s('h4/type/option/option'(A),O1) = s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,X1))) & (s('h4/type/option/option'(B),O2) = s('h4/type/option/option'(B),'h4/const/option/SOME'(s(B,X2))) & s(C,V) = s(C,happ(s(fun(B,C),happ(s(fun(A,fun(B,C)),F),s(A,X1))),s(B,X2))))))).
